Neural Networks
Model Representation

input and output
 x_{1}, x_{2} are input layers which go through a node and then generate an output layer
 h_{θ}(x) = 1 / (1 + e^{θTx})
 x_{0} is usually 1, which is also called a bias unit

sigmoid activation function
 g(z) = 1 / (1 + e^{z})

Neural network is a group of neurons put together
 hidden layers are between the input layer and the output layer
 weights are also matrix
 s_{j} units in layer j, s_{j+1} units in layer j+1
 the dimension will be s_{j+1} * (s_{j} + 1)
Intuition

Nonlinear classification
 if data can be clusterd, try to use a simple representation of a given data set
 x_{1} XOR x_{2}: true if either one is true
 x_{1} XNOR x_{2} : NOT (x_{1} XOR x_{2})
 x_{1} AND x_{2}
 do some calculation and see if the function becomes 1 with x_{1} and x_{2} are either 0 or 1